Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard

2011/10/31 by Stefan Bittner, S. Bittner, Barbara Dietz +3 · 60 citations
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Dirac (video compression format) #Dynamical billiards #Geometry #Graphene #Mathematics #Metamaterials and Metasurfaces Applications #Optics #Photonic crystal #Photonics #Physics #Quantum mechanics #Quantum optics and atomic interactions #Topological Materials and Phenomena #Zigzag #cond-mat.other #nlin.CD

paper · pdf · doi:10.1103/physrevb.85.064301

published in Physical Review B 85(6) (American Physical Society)

arxiv created 2011/12/20 · openalex publication_date 2012/02/08 · arxiv updated 2012/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders that are arranged in a triangular lattice. First, we present transmission measurements of plane waves traversing a photonic crystal. The experiments are performed in the vicinity of a Dirac point, i.e., an isolated conical singularity of the photonic band structure. There, the transmission shows a pseudodiffusive 1/L dependence, with L being the thickness of the crystal, a phenomenon also observed in graphene. Second, eigenmode intensity distributions measured in a microwave analog of a relativistic Dirac billiard, a rectangular microwave billiard that contains a photonic crystal, are discussed. Close to the Dirac point, states have been detected that are localized at the straight edge of the photonic crystal corresponding to a zigzag edge in graphene.

Citations

• Colloquium: Andreev reflection and Klein tunneling in graphene
• Sub-Poissonian Shot Noise in Graphene
• Extremal Transmission and Beating Effect of Acoustic Waves in Two-Dimensional Sonic Crystals
• Edge effects in graphene nanostructures: From multiple reflection expansion to density of states
• Band Structure of Graphite
• Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure
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• Dirac point and edge states in a microwave realization of tight-binding graphene-like structures
• Electric Field Effect in Atomically Thin Carbon Films
• Anderson localization in a string of microwave cavities
• Extremal transmission at the Dirac point of a photonic band structure
• Edge state in graphene ribbons: Nanometer size effect and edge shape dependence
• The electronic properties of graphene
• Chaotic Dirac Billiard in Graphene Quantum Dots
• Zitterbewegung, chirality, and minimal conductivity in graphene

Cited by

• Relativistic Quantum Chaos in Neutrino Billiards
• Artificial honeycomb lattices for electrons, atoms and photons